1. What is a Coterminal Angle?

Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. They differ by a full rotation (360°) or multiple rotations.

2. How Does the Calculator Work?

The calculator uses the coterminal angle formula:

Where:

• \( \theta \) — The original angle in degrees
• mod — The modulo operation that finds the remainder after division

Explanation: For any angle θ, adding or subtracting 360° will give a coterminal angle. The calculator finds the equivalent angle between 0° and 360°.

3. Importance of Coterminal Angles

Details: Coterminal angles are important in trigonometry because they have the same trigonometric function values (same sine, cosine, tangent, etc.). This simplifies calculations by allowing us to work with angles between 0° and 360°.

4. Using the Calculator

Tips: Enter any angle in degrees (positive or negative). The calculator will return the equivalent angle between 0° and 360° that shares the same terminal side.

5. Frequently Asked Questions (FAQ)

Q1: Can an angle have multiple coterminal angles?
A: Yes, any angle has infinitely many coterminal angles by adding or subtracting multiples of 360°.

Q2: What's the difference between reference and coterminal angles?
A: Coterminal angles share the same terminal side, while reference angles are the acute angle between the terminal side and the x-axis.

Q3: How are coterminal angles used in real life?
A: They're used in navigation, engineering, and physics where angle measurements might exceed 360° or be negative.

Q4: Do coterminal angles work in radians?
A: Yes, the concept is the same but using 2π radians instead of 360°.

Q5: What's the smallest positive coterminal angle?
A: It's the angle between 0° and 360° that's equivalent to the given angle, which is what this calculator finds.